+0  
 
0
31
4
avatar

What are ALL the solutions to the equation on [0,2π)?

csc(3x)=−2√3/3

 Mar 16, 2020
 #1
avatar+22085 
+1

csc is   1/sin    in quadrant III   and IV   sin is negative, so there should be two answers'

 

1/sin = -2 sqrt3/3

sin = 1/(-2 sqrt3/3)

arcsin = -60 degrees    and   240 degrees       or     240 and 300 degrees   or  4pi/3    and  5pi/3     this is   3x

 

divide the answers by 3     4pi/9   5pi/9      (edited)  

 Mar 16, 2020
edited by ElectricPavlov  Mar 16, 2020
edited by ElectricPavlov  Mar 16, 2020
 #2
avatar
0

What if all the solutions have 9,18,or 6 as a denominator?

Guest Mar 16, 2020
 #3
avatar+22085 
0

See original answer above...I edited it .....    cheeky

ElectricPavlov  Mar 16, 2020
edited by ElectricPavlov  Mar 16, 2020
 #4
avatar
0

The choices are  π/18,π/9,π/6,2π/9,7π/18,4π/9,5π/9,10π/9,11π/9,16π/9,17π/9

Guest Mar 16, 2020

7 Online Users